Superconducting fluctuation conductivity in a magnetic field in two dimensions

1985 ◽  
Vol 31 (1) ◽  
pp. 172-176 ◽  
Author(s):  
J. M. B. Lopes dos Santos ◽  
E. Abrahams
Keyword(s):  
Magnetic Field ◽  
Two Dimensions ◽  
Fluctuation Conductivity ◽  
Superconducting Fluctuation

Magnetic Field Imaging on Stacked Flash Memories by Laser Probing and SQUID Scanning

2017 ◽  
Author(s):  
K. Sanchez ◽  
G. Bascoul ◽  
F. Infante ◽  
N. Courjault ◽  
T. Nakamura
Keyword(s):  
Magnetic Field ◽  
Failure Analysis ◽  
Two Dimensions ◽  
Analysis Tool ◽  
Active Device ◽  
Current Path ◽  
3D Packaging ◽  
Magnetic Field Imaging ◽  
The Magnetic Field ◽  
Field Imaging

Abstract Magnetic field imaging is a well-known technique which gives the possibility to study the internal activity of electronic components in a contactless and non-invasive way. Additional data processing can convert the magnetic field image into a current path and give the possibility to identify current flow anomalies in electronic devices. This technique can be applied at board level or device level and is particularly suitable for the failure analysis of complex packages (stacked device & 3D packaging). This approach can be combined with thermal imaging, X-ray observation and other failure analysis tool. This paper will present two different techniques which give the possibility to measure the magnetic field in two dimensions over an active device. Same device and same level of current is used for the two techniques to give the possibility to compare the performance.

scholarly journals Levitation of non-magnetizable droplet inside ferrofluid

2018 ◽  
Vol 857 ◽  
pp. 398-448 ◽  
Author(s):  
Chamkor Singh ◽  
Arup K. Das ◽  
Prasanta K. Das
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Viscosity Ratio ◽  
Temporal Dynamics ◽  
Liquid Droplet ◽  
Droplet Surface ◽  
Two Dimensions ◽  
Projection Algorithm ◽  
The Stability ◽  
The Individual

The central theme of this work is that a stable levitation of a denser non-magnetizable liquid droplet, against gravity, inside a relatively lighter ferrofluid – a system barely considered in ferrohydrodynamics – is possible, and exhibits unique interfacial features; the stability of the levitation trajectory, however, is subject to an appropriate magnetic field modulation. We explore the shapes and the temporal dynamics of a plane non-magnetizable droplet levitating inside a ferrofluid against gravity due to a spatially complex, but systematically generated, magnetic field in two dimensions. The coupled set of Maxwell’s magnetostatic equations and the flow dynamic equations is integrated computationally, utilizing a conservative finite-volume-based second-order pressure projection algorithm combined with the front-tracking algorithm for the advection of the interface of the droplet. The dynamics of the droplet is studied under both the constant ferrofluid magnetic permeability assumption as well as for more realistic field-dependent permeability described by Langevin’s nonlinear magnetization model. Due to the non-homogeneous nature of the magnetic field, unique shapes of the droplet during its levitation, and at its steady state, are realized. The complete spatio-temporal response of the droplet is a function of the Laplace number $La$ , the magnetic Laplace number $La_{m}$ and the Galilei number $Ga$ ; through detailed simulations we separate out the individual roles played by these non-dimensional parameters. The effect of the viscosity ratio, the stability of the levitation path and the possibility of existence of multiple stable equilibrium states is investigated. We find, for certain conditions on the viscosity ratio, that there can be developments of cusps and singularities at the droplet surface; we also observe this phenomenon experimentally and compare with the simulations. Our simulations closely replicate the singular projection on the surface of the levitating droplet. Finally, we present a dynamical model for the vertical trajectory of the droplet. This model reveals a condition for the onset of levitation and the relation for the equilibrium levitation height. The linearization of the model around the steady state captures that the nature of the equilibrium point goes under a transition from being a spiral to a node depending upon the control parameters, which essentially means that the temporal route to the equilibrium can be either monotonic or undulating. The analytical model for the droplet trajectory is in close agreement with the detailed simulations.

scholarly journals Periodic self-reformation of rippled perpendicular collisionless shocks in two dimensions

2018 ◽  
Vol 36 (4) ◽  
pp. 1047-1055 ◽  
Author(s):  
Takayuki Umeda ◽  
Yuki Daicho
Keyword(s):  
Magnetic Field ◽  
Shock Front ◽  
Large Scale ◽  
Large Mass ◽  
Small Mass ◽  
Two Dimensions ◽  
Electron Mass ◽  
The Reformation ◽  
Ion Cyclotron ◽  
Mass Ratios

Abstract. Large-scale two-dimensional (2-D) full particle-in-cell (PIC) simulations are carried out for studying periodic self-reformation of a supercritical collisionless perpendicular shock with an Alfvén–Mach number MA∼6. Previous self-consistent one-dimensional (1-D) hybrid and full PIC simulations have demonstrated that the periodic reflection of upstream ions at the shock front is responsible for the formation and vanishing of the shock-foot region on a timescale of the local ion cyclotron period, which was defined as the reformation of (quasi-)perpendicular shocks. The present 2-D full PIC simulations with different ion-to-electron mass ratios show that the dynamics at the shock front is strongly modified by large-amplitude ion-scale fluctuations at the shock overshoot, which are known as ripples. In the run with a small mass ratio, the simultaneous enhancement of the shock magnetic field and the reflected ions take place quasi-periodically, which is identified as the reformation. In the runs with large mass ratios, the simultaneous enhancement of the shock magnetic field and the reflected ions occur randomly in time, and the shock magnetic field is enhanced on a timescale much shorter than the ion cyclotron period. These results indicate a coupling between the shock-front ripples and electromagnetic microinstabilities in the foot region in the runs with large mass ratios. Keywords. Space plasma physics (wave–particle interactions)

scholarly journals Modelling the Galactic magnetic field on the plane in two dimensions

2010 ◽  
Vol 401 (2) ◽  
pp. 1013-1028 ◽  
Author(s):  
T. R. Jaffe ◽  
J. P. Leahy ◽  
A. J. Banday ◽  
S. M. Leach ◽  
S. R. Lowe ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Two Dimensions ◽  
Galactic Magnetic Field

A High Accuracy of Magnetometer by Using Independent Directional Magnetic Field Measurement Technique

2014 ◽  
Vol 565 ◽  
pp. 133-137
Author(s):  
Athirot Mano ◽  
Wisut Titiroongruang
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Flux Density ◽  
Measurement Technique ◽  
Field Measurement ◽  
High Accuracy ◽  
Two Dimensions ◽  
Magnetic Flux Density ◽  
Magnetic Field Measurement ◽  
Hall Sensors

In a measurement of magnetic flux density with high accuracy by using Hall effect sensor must be considered position of Hall sensor, that perfect perpendicular with magnetic flux line for measurement. Only one Hall element can cause measuring error. Therefore, this paper presents an application of independent directional magnetic field measurement technique on two dimensions for high accuracy magnetometer. It is presented by using two Hall sensors locate perpendicular to each other and use the relation of the two voltage output signal from both Hall sensors to calculate constant Hall voltage and Magnetic flux density with high accuracy by using trigonometric function with Lab-View programming. And as the result of experiment, this technique can reduce the limitation in term of this angle in the range magnetic flux density can be measured 0-1800 gauss. A calibration curve of this system compare with standard Gauss meter shows the coefficient of determination (R2) equal to 1 and has the accuracy percentage as less than 0.5%.

Von Neumann lattices of Wannier functions for Bloch electrons in a magnetic field

1986 ◽  
Vol 403 (1824) ◽  
pp. 135-166 ◽  
Keyword(s):  
Magnetic Field ◽  
Phase Space ◽  
Periodic Function ◽  
Degrees Of Freedom ◽  
Two Dimensions ◽  
Effective Hamiltonian ◽  
Hall Conductance ◽  
Von Neumann ◽  
Wannier Functions ◽  
Bloch Electrons

The problem of Bloch electrons in a magnetic field in two dimensions can be reduced to a one-dimensional problem with a Hamiltonian Ĥ that is a periodic function of x ^ and p ^ . Wannier functions can be defined for the sub-bands of the spectrum of this effective Hamiltonian. When the Chern class (quantized Hall conductance integer) of the sub-band is zero, the Weyl-Wigner formalism can be used to represent these Wannier functions by a von Neumann lattice. It is shown how this von Neumann lattice of Wannier functions can be defined for irrational as well as rational magnetic fields. An important benefit from using the Weyl-Wigner formalism is that symmetries of the periodic potential are reflected by symmetries of the effective Hamiltonian in phase space. It is shown how the Wannier functions can be defined so that their Wigner functions have the point symmetries of the effective Hamiltonian. An example of how these results can prove useful is given: if we take matrix elements of the Hamiltonian between the Wannier states of a sub-band, we derive a new effective Hamiltonian describing this sub-band, which is again a periodic function of coordinate and momentum operators. Since, by projecting onto a sub-band, we have also reduced the number of degrees of freedom, this operation is a renormalization group transformation. It is shown that the symmetry of the new effective Hamil­tonian in phase space is the same as that of the original one. This preservation of symmetry helps to explain some unusual properties of the spectrum when the Hamiltonian has fourfold symmetry.

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